Finite Isospin Chiral Perturbation Theory in a Magnetic Field

The phase diagram of finite isospin, zero temperature QCD with the pions coupled to photons in a uniform external magnetic field is explored in the low field, small isospin density regime for which chiral perturbation theory is a valid description. For realistic pion masses, the system behaves as a type-II superconductor: a uniform superconducting state is formed at low-enough magnetic fields, a vortex state for intermediate magnetic fields and finally a normal state for large magnetic fields. In each these phases (including the vortex phase), the $\pi^{0}$ remains uncondensed just as in the zero-external field problem. The critical magnetic field where the phase transition from the uniform superconducting state to a vortex state occurs was found numerically.